10 problems

Homological detection conjecture. If

Waldhausen's conjecture. There is a finite cover $\tilde M\to M$ with $b_1(\tilde M)>0$.

Let $G$ be the fundamental group of a $3$-manifold. A non-trivial element $g\in G$ is a generalized torsion element if some non-empty finite product of conjugates of $g$ equals the…

Let $M$ be a compact $3$-manifold with prime decomposition … where the prime factors are as in (1.1) and categories (i)–(iv): the $M_i$ are closed prime $3$-manifolds with infinite…

Let $G$ be the fundamental group of a $3$--manifold. A generalized torsion element is a non-trivial element whose non-empty finite product of conjugates is the identity, and $G$ is…

Planar boundary conjecture. Every visual boundary of $G$ is planar, and furthermore, $G$ is virtually the fundamental group of a compact 3-manifold.

Let $M$ be an admissible $3$-manifold with first Betti number $b_1(M)\geq 1$. Residual local indicability conjecture. The fundamental group $\pi_1(M)$ is residually locally indicab…

Generalized-torsion conjecture. $G$ is bi-orderable if and only if $G$ has no generalized torsion element.

Mapping torus convergence-group conjecture. For any p-A-like element $\phi$ of $G$, the mapping torus subgroup $G_\phi$ acts on $S^2$ as a convergence group.

Promotion of pseudo-fibering conjecture. There are three possibilities: $G$ is elementary; $G$ is a Fuchsian group; or $G$ is a closed hyperbolic $3$-manifold group.